A graded lattice \(L\)  is semimodular iff the grading \(\rho \)  satisfies the following property:
For a general lattice \(L\)  the semimodular condition is that \(\forall a,b \in L, a \wedge b <: a\)  implies \(b <: a \vee b\) . The equivalence of two definitions can be found on standard textbooks on lattice theory, e.g. Birkoff [1]}.
\(\rho ( a \vee b) + \rho ( a \wedge b) \le \rho (a) + \rho (b) \quad \forall a, b \in L\) 
